Dark matter minispike: a significant enhancement of eccentricity for intermediate-mass-ratio-inspirals

When a stellar massive compact object, such as a black hole (BH), inspirals into an intermediate massive black hole (IMBH), an intermediate-mass-ratio-inspiral (IMRI) system forms. Such kind of systems are important sources for space-based gravitational wave detectors including LISA, Taiji and Tianqin. Dark matter (DM) minispikes may form around IMBHs. We study the effect of dynamical friction against DM minispike on the evolution of eccentric IMRI. For such investigation we construct the dynamical equations which describes the evolution of eccentric IMRI under the effect of dynamical friction. As dynamical friction is large for small velocity, the dissipation of energy near apastron is more than that near periastron. This will greatly enhance the eccentricity. For instance, with an initial semi-latus rectum of $1\rm AU$, even a moderate DM minispike can make the eccentricity grow from $0.3$ to $0.85$. In the extremal case the eccentricity could be enhanced to near $1$. We also study a specific case which corresponds to an IMRI in the center of a globular cluster (GC) and find the eccentricity can keep its value above $0.95$ until the IMRI enters LISA band. These gravitational wave with enhanced eccentricity by DM minispikes can be easly distinguished from that without DM at $10^{-3}\rm Hz$ due to the eccentricity difference. These anticipations can be tested by future space-based GW detectors such as LISA.